LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 226 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
180.1.f.a	$180$	$1$	180.f	20.d	$2$	$2$	$2$	$0.090$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{15}) $		✓	✓	✓	180.1.f.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots$
180.1.m.a	$180$	$1$	180.m	60.l	$4$	$4$	$2$	$0.090$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	180.1.m.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots$
180.1.p.a	$180$	$1$	180.p	180.p	$6$	$2$	$1$	$0.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			180.1.p.a	$4$	$0$	$-1$	$-1$	$-1$	$1$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
180.1.p.b	$180$	$1$	180.p	180.p	$6$	$2$	$1$	$0.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			180.1.p.a	$4$	$0$	$1$	$1$	$-1$	$-1$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
180.2.a.a	$180$	$2$	180.a	1.a	$1$	$1$	$1$	$1.437$	$\Q$	$_{}$	None	None	✓		✓	✓	20.2.a.a	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+2q^{13}+6q^{17}-4q^{19}+\cdots$
180.2.d.a	$180$	$2$	180.d	5.b	$2$	$2$	$2$	$1.437$	$\Q(\sqrt{-1}) $	$_{}$	None	None			✓	✓	60.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{5}+2iq^{7}+4q^{11}-2iq^{17}+\cdots$
180.2.e.a	$180$	$2$	180.e	12.b	$2$	$8$	$8$	$1.437$	8.0.18939904.2	$_{}$	None	None		✓	✓	✓	180.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{2}+\beta _{6})q^{2}+(\beta _{4}-\beta _{5}+\beta _{7})q^{4}+\cdots$
180.2.h.a	$180$	$2$	180.h	60.h	$2$	$4$	$4$	$1.437$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			180.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\zeta_{8}^{3}q^{2}+2q^{4}-\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{8}+\cdots$
180.2.h.b	$180$	$2$	180.h	60.h	$2$	$8$	$8$	$1.437$	8.0.3317760000.1	$_{}$	None	None		✓	✓		180.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{3}q^{4}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$
180.2.i.a	$180$	$2$	180.i	9.c	$3$	$2$	$1$	$1.437$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			180.2.i.a	$2$	$0$	$0$	$3$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
180.2.i.b	$180$	$2$	180.i	9.c	$3$	$6$	$3$	$1.437$	6.0.954288.1	$_{}$	None	None		✓	✓		180.2.i.b	$2$	$0$	$0$	$-1$	$3$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
180.2.j.a	$180$	$2$	180.j	15.e	$4$	$4$	$2$	$1.437$	$\Q(\zeta_{8})$	$_{}$	None	None		✓	✓	✓	180.2.j.a	$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(2-2\zeta_{8}^{2})q^{7}+\cdots$
180.2.k.a	$180$	$2$	180.k	20.e	$4$	$2$	$1$	$1.437$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			180.2.k.a	$4$	$0$	$-2$	$0$	$2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1-i)q^{2}+2iq^{4}+(1-2i)q^{5}+\cdots$
180.2.k.b	$180$	$2$	180.k	20.e	$4$	$2$	$1$	$1.437$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			180.2.k.a	$4$	$0$	$2$	$0$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1+i)q^{2}+2iq^{4}+(-1+2i)q^{5}+\cdots$
180.2.k.c	$180$	$2$	180.k	20.e	$4$	$2$	$1$	$1.437$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					20.2.e.a	$4$	$0$	$2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1+i)q^{2}+2iq^{4}+(2-i)q^{5}+(-2+\cdots)q^{8}+\cdots$
180.2.k.d	$180$	$2$	180.k	20.e	$4$	$8$	$4$	$1.437$	8.0.157351936.1	$_{}$	None	None		✓			180.2.k.d	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{2}+\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(2\beta _{4}+\cdots)q^{5}+\cdots$
180.2.k.e	$180$	$2$	180.k	20.e	$4$	$12$	$6$	$1.437$	12.0.$\cdots$.1	$_{}$	None	None			✓		60.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots$
180.2.n.a	$180$	$2$	180.n	180.n	$6$	$4$	$2$	$1.437$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			180.2.n.a	$4$	$0$	$0$	$-6$	$6$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
180.2.n.b	$180$	$2$	180.n	180.n	$6$	$4$	$2$	$1.437$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			180.2.n.a	$4$	$0$	$0$	$6$	$6$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(2+\cdots)q^{5}+\cdots$
180.2.n.c	$180$	$2$	180.n	180.n	$6$	$8$	$4$	$1.437$	8.0.3317760000.8	$_{}$	$\Q(\sqrt{-5}) $	None		✓			180.2.n.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{5}q^{2}+\beta _{1}q^{3}+2\beta _{3}q^{4}-\beta _{2}q^{5}+\cdots$
180.2.n.d	$180$	$2$	180.n	180.n	$6$	$48$	$24$	$1.437$		$_{}$	None	None		✓	✓		180.2.n.d	$8$	$0$	$0$	$0$	$-18$	$0$			$\mathrm{SU}(2)[C_{6}]$
180.2.q.a	$180$	$2$	180.q	36.h	$6$	$48$	$24$	$1.437$		$_{}$	None	None		✓	✓	✓	180.2.q.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
180.2.r.a	$180$	$2$	180.r	45.j	$6$	$12$	$6$	$1.437$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓	✓	180.2.r.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}+\beta _{9}q^{5}+(-\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{7}+\cdots$
180.2.w.a	$180$	$2$	180.w	45.l	$12$	$24$	$6$	$1.437$		$_{}$	None	None		✓	✓	✓	180.2.w.a	$4$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
180.2.x.a	$180$	$2$	180.x	180.x	$12$	$128$	$32$	$1.437$		$_{}$	None	None		✓	✓	✓	180.2.x.a	$8$	$0$	$-2$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{12}]$
180.3.b.a	$180$	$3$	180.b	15.d	$2$	$4$	$4$	$4.905$	$\Q(\sqrt{-2}, \sqrt{23})$	$_{}$	None	None		✓	✓	✓	180.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{2}q^{7}+7\beta _{1}q^{11}+\cdots$
180.3.c.a	$180$	$3$	180.c	4.b	$2$	$4$	$4$	$4.905$	$\Q(\zeta_{10})$	$_{}$	None	None					20.3.b.a	$2$	$0$	$2$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{10}q^{2}+(-1+\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{4}+\cdots$
180.3.c.b	$180$	$3$	180.c	4.b	$2$	$8$	$8$	$4.905$	8.0.85100625.1	$_{}$	None	None					60.3.c.a	$2$	$0$	$-4$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\beta _{3}q^{5}+\cdots$
180.3.c.c	$180$	$3$	180.c	4.b	$2$	$8$	$8$	$4.905$	8.0.$\cdots$.1	$_{}$	None	None		✓			180.3.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2-\beta _{4})q^{4}+\beta _{3}q^{5}+2\beta _{6}q^{7}+\cdots$
180.3.f.a	$180$	$3$	180.f	20.d	$2$	$1$	$1$	$4.905$	$\Q$	$_{}$	$\Q(\sqrt{-5}) $	None	✓				20.3.d.a	$2$	$0$	$-2$	$0$	$5$	$4$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}+5q^{5}+4q^{7}-8q^{8}+\cdots$
180.3.f.b	$180$	$3$	180.f	20.d	$2$	$1$	$1$	$4.905$	$\Q$	$_{}$	$\Q(\sqrt{-5}) $	None	✓				20.3.d.a	$2$	$0$	$2$	$0$	$5$	$-4$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+5q^{5}-4q^{7}+8q^{8}+\cdots$
180.3.f.c	$180$	$3$	180.f	20.d	$2$	$2$	$2$	$4.905$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					20.3.d.c	$4$	$0$	$0$	$0$	$-6$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{2}-4q^{4}+(-3-2i)q^{5}-4iq^{8}+\cdots$
180.3.f.d	$180$	$3$	180.f	20.d	$2$	$4$	$4$	$4.905$	$\Q(\sqrt{-3}, \sqrt{22})$	$_{}$	None	None		✓			180.3.f.d	$4$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{2})q^{2}+(-2+2\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
180.3.f.e	$180$	$3$	180.f	20.d	$2$	$4$	$4$	$4.905$	$\Q(\zeta_{12})$	$_{}$	None	None					60.3.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(2+2\zeta_{12}^{2})q^{4}+\cdots$
180.3.f.f	$180$	$3$	180.f	20.d	$2$	$4$	$4$	$4.905$	$\Q(i, \sqrt{15})$	$_{}$	$\Q(\sqrt{-15}) $	None		✓			180.3.f.f	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(4+\beta _{3})q^{4}+5\beta _{2}q^{5}+(3\beta _{1}+\cdots)q^{8}+\cdots$
180.3.f.g	$180$	$3$	180.f	20.d	$2$	$4$	$4$	$4.905$	$\Q(\sqrt{-3}, \sqrt{22})$	$_{}$	None	None		✓			180.3.f.d	$4$	$0$	$4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{2})q^{2}+(-2+2\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
180.3.f.h	$180$	$3$	180.f	20.d	$2$	$8$	$8$	$4.905$	8.0.$\cdots$.4	$_{}$	None	None			✓		60.3.f.b	$4$	$0$	$0$	$0$	$-4$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
180.3.g.a	$180$	$3$	180.g	3.b	$2$	$4$	$4$	$4.905$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		✓	✓	✓	180.3.g.a	$2$	$0$	$0$	$0$	$0$	$-16$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}+(-4-\beta _{3})q^{7}+(-\beta _{1}-6\beta _{2}+\cdots)q^{11}+\cdots$
180.3.l.a	$180$	$3$	180.l	5.c	$4$	$2$	$1$	$4.905$	$\Q(\sqrt{-1}) $	$_{}$	None	None					20.3.f.a	$2$	$0$	$0$	$0$	$6$	$-14$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(3-4i)q^{5}+(-7-7i)q^{7}-10q^{11}+\cdots$
180.3.l.b	$180$	$3$	180.l	5.c	$4$	$4$	$2$	$4.905$	$\Q(i, \sqrt{6})$	$_{}$	None	None					60.3.k.a	$2$	$0$	$0$	$0$	$-12$	$20$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-3-2\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(5+2\beta _{1}+\cdots)q^{7}+\cdots$
180.3.l.c	$180$	$3$	180.l	5.c	$4$	$4$	$2$	$4.905$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			180.3.l.c	$4$	$0$	$0$	$0$	$0$	$-4$		$5$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+(3\beta _{2}-\beta _{3})q^{11}+\cdots$
180.3.m.a	$180$	$3$	180.m	60.l	$4$	$4$	$2$	$4.905$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			180.3.m.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(4\zeta_{8}+3\zeta_{8}^{3})q^{5}+\cdots$
180.3.m.b	$180$	$3$	180.m	60.l	$4$	$4$	$2$	$4.905$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			180.3.m.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(4\zeta_{8}-3\zeta_{8}^{3})q^{5}+\cdots$
180.3.m.c	$180$	$3$	180.m	60.l	$4$	$40$	$20$	$4.905$		$_{}$	None	None		✓	✓		180.3.m.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
180.3.o.a	$180$	$3$	180.o	9.d	$6$	$4$	$2$	$4.905$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	None	None		✓			180.3.o.a	$2$	$0$	$0$	$-6$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-3+3\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
180.3.o.b	$180$	$3$	180.o	9.d	$6$	$12$	$6$	$4.905$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		180.3.o.b	$2$	$0$	$0$	$2$	$0$	$-6$		$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}+\beta _{8}q^{5}+(\beta _{1}+\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots$
180.3.p.a	$180$	$3$	180.p	180.p	$6$	$4$	$2$	$4.905$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			180.3.p.a	$4$	$0$	$-4$	$4$	$10$	$4$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-2+2\beta _{2})q^{2}+(\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots$
180.3.p.b	$180$	$3$	180.p	180.p	$6$	$4$	$2$	$4.905$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			180.3.p.a	$4$	$0$	$4$	$-4$	$10$	$-4$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(2-2\beta _{2})q^{2}+(\beta _{1}-2\beta _{2}-\beta _{3})q^{3}+\cdots$
180.3.p.c	$180$	$3$	180.p	180.p	$6$	$128$	$64$	$4.905$		$_{}$	None	None		✓	✓		180.3.p.c	$8$	$0$	$0$	$0$	$-22$	$0$			$\mathrm{SU}(2)[C_{6}]$
180.3.s.a	$180$	$3$	180.s	36.f	$6$	$96$	$48$	$4.905$		$_{}$	None	None		✓	✓	✓	180.3.s.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.